In this paper we introduce the monotonic modal logics M4wn, M4n and MBn obtained from the basic strong monotonic modal logic MON by adding some formulas considered by R. Jansana in [8]. For each logic defined we prove completeness with respect to their characteristic classes of monotonic frames. The canonicity of these logics is proved using the representation theory for monotonic algebras deve...

The problem of iterative roots for strictly monotone self-mappings has been well solved. Most of known results concerning existence of iterative roots for a continuous function were given under the assumption that the function has finitely many non-monotonic points. When a function has infinitely many non-monotonic points, the problem of the existence of its iterative roots will become more com...